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Volume 6, Issue 1, Article 17 |
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A Stochastic Gronwall Inequality and Its Applications
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Authors: |
Kazuo Amano, |
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Keywords:
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Gronwall inequality, Ito integral |
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Date Received:
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15/12/04 |
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Date Accepted:
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01/02/05 |
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Subject Codes: |
26D10, 26D20, 60H05, 60H35
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Editors: |
Sever S. Dragomir, |
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Abstract: |
In this paper, we show a Gronwall type inequality for Ito integrals (Theorems 1.1 and 1.2) and give some applications. Our inequality gives a simple proof of the existence theorem for stochastic differential equation (Example 2.1) and also, the error estimate of Euler-Maruyama scheme follows immediately from our result (Example 2.2}).
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